There are only a couple assumptions, everything else is derived from objective evidence and those assumptions.
The thing is, even if you grant the assumptions as the basis for both C14 dating and supernova studies, it seems quite miraculous, if you'll excuse the term, that those two assumptions which have nothing to do with one another at first, end up showing the exact same thing. It's almost as if...dare I say it...the assumptions were right. So while Creationists may be able to jump on the "but those are based on assumptions" bandwagon and get some traction, they can't argue they're wrong until they show us their own assumptions that lead to consistent results across multiple disciplines.
For example, if we somehow assume that decay rates have changed, how does that effect the dates of specimens we've studied? Once you have those conclusions, what does that say about the supernova measurements? What do those assumptions say about radioactivity halos? You can't make an assumption to "fix" one scientific answer without altering a whole host of other ones. Those other conclusions will rapidly degenerate into conflicting consequences, or at least make it at least as improbable as before that the creationist's beliefs were right.